TWO GENERALIZATIONS OF LCM-STABLE EXTENSIONS
TWO GENERALIZATIONS OF LCM-STABLE EXTENSIONS
Let <TEX>$R{\subseteq}T$</TEX> be an extension of integral domains, X be an indeterminate over T, and R[X] and T[X] be polynomial rings. Then <TEX>$R{\subseteq}T$</TEX> is said to be LCM-stable if <TEX>$(aR{\cap}bR)T=aT{\cap}bT$</TEX> for all <TEX>$0{\neq}a,b{\in}R$</TEX>. Let <TEX>$w_A$</TEX> be the so-called <TEX>$w$</TEX>-operation on an integral domain A. In this paper, we introduce the …